geometry: part 2

Geometry: Part 2Geometry: Part 23-D figures3-D figures

PolyhedronPolyhedron►3-dimensional analog of a polygon3-dimensional analog of a polygon►Closed surface made up of polygonsClosed surface made up of polygons►Any 2 polygons may have only one Any 2 polygons may have only one

shared edgeshared edge

Face

EdgeVertex

PrismPrism► Polyhedron with 2 opposite faces that Polyhedron with 2 opposite faces that

are identical polygonsare identical polygons

►Faces are called basesFaces are called bases

►Bases are joined by lateral faces Bases are joined by lateral faces If the lateral face is a rectangle it is a If the lateral face is a rectangle it is a right right

prismprism

Examples:Examples:► 2 hexagons for 2 hexagons for

basesbases► Right Hexagonal Right Hexagonal

prismprism

► 2 rectangles for 2 rectangles for basesbases

► Right rectangular Right rectangular prismprism

base

Lateral face

Geometry in the Real World Geometry in the Real World

PyramidPyramid

► Base is any regular Base is any regular polygonpolygon

► All sides are All sides are trianglestriangles

Platonic SolidsPlatonic Solids►All sides are equalAll sides are equal►All angles are the sameAll angles are the same►All faces are identicalAll faces are identical►Same number of polygons meet at Same number of polygons meet at

each vertexeach vertex►Only five solids meet these criteria: Only five solids meet these criteria:

Platonic solidsPlatonic solids

TetrahedronTetrahedron► Composed of 4 Composed of 4

equilateral trianglesequilateral triangles► 3 triangles meet at 3 triangles meet at

vertexvertex► Represented fire to Represented fire to

the ancient Greeksthe ancient Greeks

Hexahedron (Cube)Hexahedron (Cube)► Composed of 6 Composed of 6

squaressquares► 3 squares meet at a 3 squares meet at a

vertexvertex► Represented the Represented the

stable earthstable earth

OctahedronOctahedron► Composed of 8 Composed of 8

equilateral trianglesequilateral triangles► 4 triangles meet at 4 triangles meet at

a vertexa vertex► Represented airRepresented air

DodecahedronDodecahedron► Composed of 12 Composed of 12

equilateral equilateral pentagonspentagons

► 3 pentagons meet 3 pentagons meet at a vertexat a vertex

► Represented the 12 Represented the 12 signs of the Zodiacsigns of the Zodiac

IcosahedronIcosahedron► Composed of 20 Composed of 20

equilateral trianglesequilateral triangles► 5 triangles meet at 5 triangles meet at

a vertexa vertex► Represented waterRepresented water

Models of PolyhedraModels of Polyhedra